典型例題分析1: 已知拋物線y=x2﹣2mx+m2+m﹣1(m是常數(shù))的頂點(diǎn)為P,直線l:y=x﹣1. (1)求證:點(diǎn)P在直線l上; (2)當(dāng)m=﹣3時(shí),拋物線與x軸交于A,B兩點(diǎn),與y軸交于點(diǎn)C,與直線l的另一個(gè)交點(diǎn)為Q,M是x軸下方拋物線上的一點(diǎn),∠ACM=∠PAQ(如圖),求點(diǎn)M的坐標(biāo); (3)若以拋物線和直線l的兩個(gè)交點(diǎn)及坐標(biāo)原點(diǎn)為頂點(diǎn)的三角形是等腰三角形,請直接寫出所有符合條件的m的值. ![](http://image109.360doc.com/DownloadImg/2020/09/0312/201193561_1_20200903121246677_wm)
![](http://image109.360doc.com/DownloadImg/2020/09/0312/201193561_2_20200903121246865_wm)
![](http://image109.360doc.com/DownloadImg/2020/09/0312/201193561_3_2020090312124737_wm)
![](http://image109.360doc.com/DownloadImg/2020/09/0312/201193561_4_20200903121247302_wm) 如圖,直線AB分別交y軸、x軸于A、B兩點(diǎn),OA=2,tan∠ABO=1/2,拋物線y=﹣x2+bx+c過A、B兩點(diǎn).(2)設(shè)拋物線的頂點(diǎn)為D,求△ABD的面積;(3)作垂直x軸的直線x=t,在第一象限交直線AB于M,交這個(gè)拋物線于N.求當(dāng)t取何值時(shí),MN的長度l有最大值?最大值是多少?![](http://image109.360doc.com/DownloadImg/2020/09/0312/201193561_5_20200903121247537_wm)
![](http://image109.360doc.com/DownloadImg/2020/09/0312/201193561_6_20200903121247787_wm)
![](http://image109.360doc.com/DownloadImg/2020/09/0312/201193561_7_20200903121247990_wm) (1)求出OB,把A、B的坐標(biāo)代入y=﹣x2+bx+c和y=kx+e求出即可;(2)求出D的坐標(biāo),再根據(jù)面積公式求出即可;(3)求出M、N的坐標(biāo),求出MN的值,再化成頂點(diǎn)式,即可求出答案.
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